| import OAI.Analysis.IrrationalRotation.Model.ProductCoupling | |
| namespace OAI | |
| noncomputable section | |
| namespace Invariant233.OrderedProductCoupling | |
| def sourceKappa (s : ℕ) : ℝ := 1 / (100 * ((s : ℝ) + 1)) | |
| def ofBlocks (m : ℕ → ℕ) (κ a b : ℕ → ℝ) | |
| (hκ0 : ∀ s, 0 ≤ κ s) (hκ : ∀ s, κ s ≤ 1 / 100) | |
| (hm : ∀ s, 100 ≤ m s) | |
| (ha : ∀ s, 1 / (m s : ℝ) ≤ a s) (ha' : ∀ s, a s ≤ 1 / 4) | |
| (hb : ∀ s, 1 / (m s : ℝ) ≤ b s) (hb' : ∀ s, b s ≤ 1 / 4) | |
| (e : ℕ ≃ Σ s, Fin (m s)) (tag : ℕ) : Parameters where | |
| κ i := κ (e i).1 | |
| m i := m (e i).1 | |
| a i := a (e i).1 | |
| b i := b (e i).1 | |
| t i := if (e i).1 = tag then 1 else 0 | |
| κ_nonneg i := hκ0 (e i).1 | |
| κ_le i := hκ (e i).1 | |
| m_ge i := by exact_mod_cast hm (e i).1 | |
| a_lower i := ha (e i).1 | |
| a_upper i := ha' (e i).1 | |
| b_lower i := hb (e i).1 | |
| b_upper i := hb' (e i).1 | |
| t_nonneg i := by split_ifs <;> norm_num | |
| t_le i := by split_ifs <;> norm_num | |
| def blockDensityBound (κ : ℕ → ℝ) : ℝ := | |
| Real.exp (10 * (2 * (∑' s, κ s ^ 2) + 1)) | |
| end Invariant233.OrderedProductCoupling | |
| end | |
| end OAI | |